Finite Group Databasebeta

← C3×D3×#805 #13157408

Subgroups — C3×D3×#805 #13157408

Order 1728.

906 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic
2C32×C42×D3C211yesmaximal, characteristic, complemented
3C3×D3×#208C211yesmaximal, characteristic, complemented
4C3×#63632C211yesmaximal, characteristic, complemented
5C32×#805C211yesmaximal, characteristic, complemented
6C3×#63570C211yesmaximal, characteristic, complemented
7C3×#63569C211yesmaximal, characteristic, complemented
8C2×C3×#805—31nomaximal
9C3×D3×#104—31nomaximal
10D3×#805C311yesmaximal, characteristic, direct product factor
11C3×#3828C2211yescharacteristic
12C32×#235C2211yescharacteristic
13C2×C32×C4×D3—21no—
14C2×C32×C4×D3C2211yescharacteristic
15C3×D3×#67—21no—
16C3×#3804—21no—
17C3×D3×D12C411yescharacteristic, complemented
18C3×C4×D32—21no—
19C3×#3799C411yescharacteristic, complemented
20C3×#3798—21no—
21C3×#3795C411yescharacteristic, complemented
22C3×D3×Dic6C411yescharacteristic, complemented
23C33×C42C2211yescharacteristic, complemented
24C3×#3748C2211yescharacteristic, complemented
25C32×C4×Dic3—21no—
26C32×C4×Dic3C2211yescharacteristic, complemented
27C32×#208C2211yescharacteristic, complemented
28C3×#3711—21no—
29C3×D3×C3⋊C8—21no—
30C3×D3×#41—31no—
31C2×C3×#235—31no—
32D3×#235C2×C311yescharacteristic
33C2×C32×C42—31no—
34C2×C3×#208—31no—
35C3×D3×M16—31no—
36C3×C42×D3—21no—
37C3×C42×D3D311yescharacteristic, complemented
38C3×C42×D3C2×C311yescharacteristic, complemented
39D3×#208C2×C311yescharacteristic, complemented
40C32×#104—31no—
41#63632C2×C311yescharacteristic, complemented
42C3×#837—31no—
43C3×#825—31no—
44C3×#805—21no—
45C3×#805—31no—
46C3×#805—31no—
47C3×#805—31no—
48C3×#805—31no—
49C3×#805—61no—
50C3×#805D311yescharacteristic, direct product factor
51C3×#805C2×C311yescharacteristic, complemented
52#63570C2×C311yescharacteristic, complemented
53#63569C2×C311yescharacteristic, complemented
54C22×C32×D3D411yescharacteristic
55C2×C3×D32—21no—
56C2×C33×C4—21no—
57C2×C33×C4C2311yescharacteristic
58C3×#638—21no—
59C3×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
60C3×C4×C3⋊D3—21no—
61C3×#634C2×C411yescharacteristic, complemented
62C32×#67—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3D411yescharacteristic
65C32×D12C2×C411yescharacteristic, complemented
66C32×C4×D3—24no—
67C32×C4×D3—21no—
68C32×C4×D3C2×C411yescharacteristic
69C32×C4×D3C2×C411yescharacteristic
70C32×C4×D3D411yescharacteristic
71C32×C4×D3D411yescharacteristic
72C32×Dic6C2×C411yescharacteristic, complemented
73C3×#627—21no—
74C3×#626—21no—
75C3×#626—21no—
76C3×#625—21no—
77C3×#624—21no—
78C3×D3×Dic3—21no—
79C3×D3×Dic3—21no—
80C3×C3⋊(C3⋊C8)—21no—
81C32×C3⋊C8—21no—
82C2×C3×#104—91no—
83C2×#805—31no—
84D3×#104—31no—
85C32×#41—31no—
86C22×C32×C4—31no—
87C22×C32×C4—61no—
88#3828C22×C311yescharacteristic
89C2×C3×#67—61no—
90C3×#239—31no—
91C3×D3×Q8—31no—
92C3×#237—31no—
93C3×#237—61no—
94C3×D3×D4—31no—
95C3×D3×D4—61no—
96C3×#235—21no—
97C3×#235—31no—
98C3×#235—31no—
99C3×#235—31no—
100C3×#235—31no—
101C3×#235—61no—
102C3×#235—61no—
103C3×#235—61no—
104C3×#235—61no—
105C3×#235C2×D311yescharacteristic
106C3×#235C22×C311yescharacteristic
107C2×C3×D12—31no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—61no—
113C2×C3×C4×D3—61no—
114C2×C3×C4×D3C2×D311yescharacteristic
115C2×C3×C4×D3C22×C311yescharacteristic
116C2×C3×Dic6—31no—
117D3×#67—21no—
118#3804—21no—
119D3×D12C3×C411yescharacteristic, complemented
120C4×D32—21no—
121#3799C3×C411yescharacteristic, complemented
122#3798—21no—
123#3795C3×C411yescharacteristic, complemented
124D3×Dic6C3×C411yescharacteristic, complemented
125C32×M16—31no—
126C32×C42—21no—
127C32×C42—21no—
128C32×C42—21no—
129C32×C42—31no—
130C32×C42—41no—
131C32×C42—61no—
132C32×C42C2×D311yescharacteristic, complemented
133C32×C42C2×D311yescharacteristic, complemented
134C32×C42C22×C311yescharacteristic, complemented
135#3748C22×C311yescharacteristic, complemented
136C3×C4×Dic3—22no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2×D311yescharacteristic, complemented
141C3×C4×Dic3C22×C311yescharacteristic, complemented
142C3×#208—21no—
143C3×#208—31no—
144C3×#208—31no—
145C3×#208—61no—
146C3×#208—61no—
147C3×#208C2×D311yescharacteristic, complemented
148C3×#208C22×C311yescharacteristic, complemented
149C2×C3×C3⋊C8—61no—
150C3×ΓL(1,𝔽25)—61no—
151C3×D3×C8—61no—
152#3711—21no—
153D3×C3⋊C8—21no—
154C22×C33C2×D411yescharacteristic
155C2×C3×C3⋊D3—21no—
156C2×C32×D3—22no—
157C2×C32×D3—21no—
158C2×C32×D3C22⋊C411yescharacteristic
159C2×C32×D3C22⋊C411yescharacteristic
160C3×D32—42no—
161C33×C4—22no—
162C33×C4C22×C411yescharacteristic
163C33×C4C2×D411yescharacteristic
164C3×C3⋊Dic3—21no—
165C32×Dic3—22no—
166C32×Dic3—21no—
167C32×Dic3C22⋊C411yescharacteristic
168C32×Dic3C22⋊C411yescharacteristic
169C2×C3×#41—91no—
170D3×#41—31no—
171C2×#235—31no—
172C2×C3×M16—91no—
173C2×C3×C42—31no—
174C2×C3×C42—31no—
175C2×C3×C42—61no—
176C2×#208—31no—
177D3×M16—31no—
178C42×D3C3×D311yescharacteristic, complemented
179C3×#104—31no—
180C3×#104—31no—
181C3×#104—61no—
182C3×#104—91no—
183C3×#104—91no—
184C3×#104—91no—
185#837—31no—
186#825—31no—
187#805—31no—
188#805—31no—
189#805—31no—
190#805—31no—
191#805—61no—
192#805C3×D311yescharacteristic, direct product factor
193C23×C32—31no—
194C22×C3×D3—21no—
195C22×C3×D3—61no—
196C22×C3×D3—61no—
197C22×C3×D3#6711yescharacteristic
198C22×C3×D3C3×D411yescharacteristic
199C2×D32—21no—
200C32×Q8—31no—
201C32×D4—31no—
202C32×D4—61no—
203C2×C32×C4—21no—
204C2×C32×C4—22no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—31no—
211C2×C32×C4—31no—
212C2×C32×C4—31no—
213C2×C32×C4—31no—
214C2×C32×C4—31no—
215C2×C32×C4—41no—
216C2×C32×C4—41no—
217C2×C32×C4—41no—
218C2×C32×C4—42no—
219C2×C32×C4—64no—
220C2×C32×C4—61no—
221C2×C32×C4—61no—
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C23×C311yescharacteristic
225#638—21no—
226C4⋊(C3⋊D3)C2×C3×C411yescharacteristic, complemented
227C4×C3⋊D3—21no—
228#634C2×C3×C411yescharacteristic, complemented
229C3×#67—21no—
230C3×#67—21no—
231C3×#67—41no—
232C3×#67—61no—
233C3×#67—61no—
234C3×#67—61no—
235C3×#67—61no—
236C3×#67—61no—
237C3×#67—61no—
238C3×#67—121no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3#6711yescharacteristic
246C2×C3×Dic3C3×D411yescharacteristic
247C3×D12—21no—
248C3×D12—31no—
249C3×D12—31no—
250C3×D12—61no—
251C3×D12—61no—
252C3×D12—61no—
253C3×D12C4×D311yescharacteristic, complemented
254C3×D12C2×C3×C411yescharacteristic, complemented
255C3×C4×D3—28no—
256C3×C4×D3—24no—
257C3×C4×D3—24no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—41no—
265C3×C4×D3—61no—
266C3×C4×D3—61no—
267C3×C4×D3—61no—
268C3×C4×D3—61no—
269C3×C4×D3—61no—
270C3×C4×D3—61no—
271C3×C4×D3—121no—
272C3×C4×D3C4×D311yescharacteristic
273C3×C4×D3C4×D311yescharacteristic
274C3×C4×D3D1211yescharacteristic
275C3×C4×D3D1211yescharacteristic
276C3×C4×D3C2×C3×C411yescharacteristic
277C3×C4×D3C2×C3×C411yescharacteristic
278C3×C4×D3C3×D411yescharacteristic
279C3×C4×D3C3×D411yescharacteristic
280C3×Dic6—21no—
281C3×Dic6—31no—
282C3×Dic6—31no—
283C3×Dic6—61no—
284C3×Dic6—61no—
285C3×Dic6—61no—
286C3×Dic6C4×D311yescharacteristic, complemented
287C3×Dic6C2×C3×C411yescharacteristic, complemented
288#627—21no—
289#626—21no—
290#626—21no—
291#625—21no—
292#624—21no—
293D3×Dic3—21no—
294D3×Dic3—21no—
295C32×C8—61no—
296C3⋊(C3⋊C8)—21no—
297C3×C3⋊C8—21no—
298C3×C3⋊C8—21no—
299C3×C3⋊C8—41no—
300C3×C3⋊C8—61no—
301C3×C3⋊C8—61no—
302C3×C3⋊C8—121no—
303C2×#104—91noSylow
304C2×C33—21no—
305C2×C33C2×C22⋊C411yescharacteristic
306C3×C3⋊D3—41no—
307C32×D3—21no—
308C32×D3—41no—
309C32×D3#10412yescomplemented
310C3×#41—31no—
311C3×#41—31no—
312C3×#41—61no—
313C3×#41—91no—
314C3×#41—91no—
315C3×#41—91no—
316C3×#41—181no—
317C3×#41—181no—
318C2×C3×Q8—91no—
319C2×C3×D4—91no—
320C2×C3×D4—181no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—62no—
327C22×C3×C4—181no—
328C2×#67—61no—
329#239—31no—
330D3×Q8—31no—
331#237—31no—
332#237—61no—
333D3×D4—31no—
334D3×D4—61no—
335#235—31no—
336#235—31no—
337#235—31no—
338#235—31no—
339#235—61no—
340#235—61no—
341#235—61no—
342#235—61no—
343#235C2×C3×D311yescharacteristic
344C2×D12—31no—
345C2×C4×D3—21no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C2×C3×D311yescharacteristic
349C2×Dic6—31no—
350C3×M16—31no—
351C3×M16—31no—
352C3×M16—61no—
353C3×M16—91no—
354C3×M16—181no—
355C2×C3×C8—181no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—41no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365C3×C42—62no—
366C3×C42D3211yescharacteristic, complemented
367C3×C42C2×C3×D311yescharacteristic, complemented
368C3×C42C2×C3×D311yescharacteristic, complemented
369C4×Dic3—21no—
370C4×Dic3C2×C3×D311yescharacteristic, complemented
371#208—31no—
372#208—31no—
373#208—61no—
374#208—61no—
375#208C2×C3×D311yescharacteristic, complemented
376C2×C3⋊C8—61no—
377ΓL(1,𝔽25)—61no—
378D3×C8—61no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—31no—
383C22×C32—31no—
384C22×C32—41no—
385C22×C32—62no—
386C22×C32—61no—
387C22×C32D3×D411yescharacteristic
388C22×C32C2×#6711yescharacteristic
389C22×C32C2×C3×D411yescharacteristic
390C2×C3⋊D3—21no—
391C2×C3×D3—24no—
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—41no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
401C2×C3×D3—121no—
402C2×C3×D3—122no—
403C2×C3×D3—122no—
404C2×C3×D3(C2×D3)⋊C411yescharacteristic
405C2×C3×D3(C2×D3)⋊C411yescharacteristic
406C2×C3×D3C3×C22⋊C411yescharacteristic
407C2×C3×D3C3×C22⋊C411yescharacteristic
408D32—42no—
409C32×C4—22no—
410C32×C4—24no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—21no—
419C32×C4—31no—
420C32×C4—31no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4—42no—
424C32×C4—42no—
425C32×C4—44no—
426C32×C4—62no—
427C32×C4—61no—
428C32×C4C2×C4×D311yescharacteristic
429C32×C4C2×C4×D311yescharacteristic
430C32×C4C2×D1211yescharacteristic
431C32×C4D3×D411yescharacteristic
432C32×C4C22×C3×C411yescharacteristic
433C32×C4C2×C3×D411yescharacteristic
434C3⋊Dic3—21no—
435C3×Dic3—24no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—21no—
442C3×Dic3—41no—
443C3×Dic3—61no—
444C3×Dic3—61no—
445C3×Dic3—121no—
446C3×Dic3(C2×D3)⋊C411yescharacteristic
447C3×Dic3(C2×D3)⋊C411yescharacteristic
448C3×Dic3C3×C22⋊C411yescharacteristic
449C3×Dic3C3×C22⋊C411yescharacteristic
450C2×#41—91no—
451C2×M16—91no—
452C2×C42—31no—
453#104—31no—
454#104—91no—
455#104—91no—
456#104—91no—
457C33C2×#10411yescharacteristic, complemented, Sylow
458C23×C3—31no—
459C23×C3—31no—
460C23×C3—61no—
461C23×C3—181no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3C3×#6711yescharacteristic
465C3×Q8—31no—
466C3×Q8—31no—
467C3×Q8—61no—
468C3×Q8—91no—
469C3×Q8—181no—
470C3×D4—31no—
471C3×D4—31no—
472C3×D4—61no—
473C3×D4—61no—
474C3×D4—61no—
475C3×D4—91no—
476C3×D4—121no—
477C3×D4—181no—
478C3×D4—181no—
479C3×D4—181no—
480C3×D4—181no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—42no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—64no—
508C2×C3×C4—64no—
509C2×C3×C4—68no—
510C2×C3×C4—62no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—121no—
516C2×C3×C4—181no—
517C2×C3×C4—181no—
518C2×C3×C4—181no—
519C2×C3×C4—181no—
520C2×C3×C4C2×D3211yescharacteristic
521C2×C3×C4C22×C3×D311yescharacteristic
522C2×C3×C4C22×C3×D311yescharacteristic
523#67—21no—
524#67—61no—
525#67—61no—
526#67—61no—
527#67—61no—
528#67—61no—
529#67—61no—
530#67—121no—
531C2×Dic3—21no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3C3×#6711yescharacteristic
535D12—31no—
536D12—31no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12C3×C4×D311yescharacteristic, complemented
541C4×D3—24no—
542C4×D3—21no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—121no—
550C4×D3C3×C4×D311yescharacteristic
551C4×D3C3×C4×D311yescharacteristic
552C4×D3C3×D1211yescharacteristic
553C4×D3C3×D1211yescharacteristic
554Dic6—31no—
555Dic6—31no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6C3×C4×D311yescharacteristic, complemented
560C3×C8—61no—
561C3×C8—61no—
562C3×C8—121no—
563C3×C8—181no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—121no—
568C2×C32—21no—
569C2×C32—22no—
570C2×C32—21no—
571C2×C32—21no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32—32no—
576C2×C32—41no—
577C2×C32—41no—
578C2×C32—41no—
579C2×C32—42no—
580C2×C32—61no—
581C2×C32—121no—
582C2×C32D3×C22⋊C411yescharacteristic
583C2×C32C2×(C2×D3)⋊C411yescharacteristic
584C2×C32C2×C3×C22⋊C411yescharacteristic
585C3⋊D3—41no—
586C3×D3—22no—
587C3×D3—21no—
588C3×D3—21no—
589C3×D3—22no—
590C3×D3—41no—
591C3×D3—41no—
592C3×D3—81no—
593C3×D3—121no—
594C3×D3—121no—
595C3×D3—241no—
596C3×D3#80512yesdirect product factor
597C3×D3C3×#10412yescomplemented
598#41—31no—
599#41—91no—
600#41—91no—
601#41—91no—
602#41—181no—
603#41—181no—
604C2×Q8—91no—
605C2×D4—91no—
606C2×D4—181no—
607C22×C4—31no—
608C22×C4—61no—
609C22×C4—181no—
610M16—31no—
611M16—91no—
612M16—181no—
613C2×C8—181no—
614C42—31no—
615C42—61no—
616C42C3×D3211yescharacteristic, complemented
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—31no—
621C22×C3—31no—
622C22×C3—31no—
623C22×C3—31no—
624C22×C3—41no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—62no—
628C22×C3—62no—
629C22×C3—64no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—121no—
633C22×C3—181no—
634C22×C3—362no—
635C22×C3D3×#6711yescharacteristic
636C22×C3C3×D3×D411yescharacteristic
637C22×C3C2×C3×#6711yescharacteristic
638C2×D3—22no—
639C2×D3—21no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—121no—
643C2×D3—122no—
644C2×D3—122no—
645C2×D3C3×(C2×D3)⋊C411yescharacteristic
646C2×D3C3×(C2×D3)⋊C411yescharacteristic
647C3×C4—22no—
648C3×C4—24no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—31no—
658C3×C4—31no—
659C3×C4—31no—
660C3×C4—31no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—44no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—64no—
669C3×C4—62no—
670C3×C4—62no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—121no—
674C3×C4—181no—
675C3×C4C4×D3211yescharacteristic
676C3×C4D3×D1211yescharacteristic
677C3×C4C2×C3×C4×D311yescharacteristic
678C3×C4C2×C3×C4×D311yescharacteristic
679C3×C4C2×C3×D1211yescharacteristic
680C3×C4C3×D3×D411yescharacteristic
681Dic3—22no—
682Dic3—21no—
683Dic3—61no—
684Dic3—61no—
685Dic3—121no—
686Dic3C3×(C2×D3)⋊C411yescharacteristic
687Dic3C3×(C2×D3)⋊C411yescharacteristic
688C32—21no—
689C32—21no—
690C32—21no—
691C32—41no—
692C32D3×#10411yescharacteristic, complemented
693C32C2×#80511yescharacteristic, complemented
694C32C2×C3×#10411yescharacteristic, complemented
695C23—31no—
696C23—181no—
697Q8—31no—
698Q8—91no—
699Q8—181no—
700D4—31no—
701D4—61no—
702D4—91no—
703D4—181no—
704D4—181no—
705D4—181no—
706D4—181no—
707C2×C4—21no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—64no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4C2×C3×D3211yescharacteristic
721C8—61no—
722C8—181no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—32no—
731C2×C3—32no—
732C2×C3—41no—
733C2×C3—41no—
734C2×C3—42no—
735C2×C3—41no—
736C2×C3—62no—
737C2×C3—62no—
738C2×C3—61no—
739C2×C3—61no—
740C2×C3—121no—
741C2×C3—121no—
742C2×C3—241no—
743C2×C3—361no—
744C2×C3D3×(C2×D3)⋊C411yescharacteristic
745C2×C3C3×D3×C22⋊C411yescharacteristic
746C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
747D3—21no—
748D3—41no—
749D3—121no—
750D3—121no—
751D3—241no—
752D3C3×#80512yesdirect product factor
753C22—31no—
754C22—31no—
755C22—62no—
756C22—61no—
757C22—181no—
758C22—362no—
759C22C3×D3×#6711yescharacteristic
760C4—22no—
761C4—31no—
762C4—31no—
763C4—62no—
764C4—61no—
765C4—181no—
766C4C3×C4×D3211yescharacteristic
767C4C3×D3×D1211yescharacteristic
768C3—21no—
769C3—21no—
770C3—21no—
771C3—41no—
772C3D3×#80511yescharacteristic, direct product factor
773C3C3×D3×#10411yescharacteristic, complemented
774C3C2×C3×#80511yescharacteristic, complemented
775C2—21no—
776C2—32no—
777C2—61no—
778C2—121no—
779C2—361no—
780C2C3×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC3×C4D3×D12
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC2×C33C2×C22⋊C4
prime radicalC3×D3×#235C2
cosocleC2×C32×C4C23×C3
hypercenterC3×C42D32
hypocenterC32C2×C3×#104
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C32×C42×D3C2semidirect
3. C3×D3×#208C2semidirect
4. C3×#63632C2semidirect
5. C32×#805C2semidirect
6. C3×#63570C2semidirect
7. C3×#63569C2semidirect
10. D3×#805C3direct (N × H)
17. C3×D3×D12C4semidirect
19. C3×#3799C4semidirect
21. C3×#3795C4semidirect
22. C3×D3×Dic6C4semidirect
23. C33×C42C22semidirect
24. C3×#3748C22semidirect
26. C32×C4×Dic3C22semidirect
27. C32×#208C22semidirect
37. C3×C42×D3D3semidirect
38. C3×C42×D3C2×C3semidirect
39. D3×#208C2×C3semidirect
41. #63632C2×C3semidirect
50. C3×#805D3direct (N × H)
51. C3×#805C2×C3semidirect
52. #63570C2×C3semidirect
53. #63569C2×C3semidirect
59. C3×C4⋊(C3⋊D3)C2×C4semidirect
61. C3×#634C2×C4semidirect
65. C32×D12C2×C4semidirect
72. C32×Dic6C2×C4semidirect
119. D3×D12C3×C4semidirect
121. #3799C3×C4semidirect
123. #3795C3×C4semidirect
124. D3×Dic6C3×C4semidirect
132. C32×C42C2×D3semidirect
133. C32×C42C2×D3semidirect
134. C32×C42C22×C3semidirect
135. #3748C22×C3semidirect
140. C3×C4×Dic3C2×D3semidirect
141. C3×C4×Dic3C22×C3semidirect
147. C3×#208C2×D3semidirect
148. C3×#208C22×C3semidirect
178. C42×D3C3×D3semidirect
192. #805C3×D3direct (N × H)
226. C4⋊(C3⋊D3)C2×C3×C4semidirect
228. #634C2×C3×C4semidirect
253. C3×D12C4×D3semidirect
254. C3×D12C2×C3×C4semidirect
286. C3×Dic6C4×D3semidirect
287. C3×Dic6C2×C3×C4semidirect
309. C32×D3#104semidirect
366. C3×C42D32semidirect
367. C3×C42C2×C3×D3semidirect
368. C3×C42C2×C3×D3semidirect
370. C4×Dic3C2×C3×D3semidirect
375. #208C2×C3×D3semidirect
457. C33C2×#104semidirect
540. D12C3×C4×D3semidirect
559. Dic6C3×C4×D3semidirect
596. C3×D3#805direct (N × H)
597. C3×D3C3×#104semidirect
616. C42C3×D32semidirect
692. C32D3×#104semidirect
693. C32C2×#805semidirect
694. C32C2×C3×#104semidirect
752. D3C3×#805direct (N × H)
772. C3D3×#805direct (N × H)
773. C3C3×D3×#104semidirect
774. C3C2×C3×#805semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×D3×#2352
C32×C42×D32
C3×D3×#2082
C3×#636322
C32×#8052
C3×#635702
C3×#635692
C2×C3×#8053
C3×D3×#1043
D3×#8053